Energy Systems

, Volume 3, Issue 3, pp 221–258 | Cite as

Optimal power flow: a bibliographic survey I

Formulations and deterministic methods
  • Stephen Frank
  • Ingrida Steponavice
  • Steffen Rebennack
Original Paper

Abstract

Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

Keywords

Electric power systems Optimal power flow Optimal power flow formulations Optimal power flow requirements Deterministic optimization Global optimization Nonlinear optimization Survey 

Abbreviations

The following summarizes the meanings of abbreviations and acronyms used throughout the paper:

AC

Alternating Current

ASP

Active Set and Penalty

BFGS

Broyden-Fletcher-Goldfarb-Shanno (quasi-Newton method)

CG

Conjugate Gradient

DC

Direct Current

DFP

Davidon-Fletcher-Powell (quasi-Newton method)

ECQ

Extended Conic-Quadratic

HVDC

High-Voltage Direct Current

FACTS

Flexible AC Transmission Systems

GRG

Generalized Reduced Gradient

IPM

Interior Point Method

KKT

Karush-Kuhn-Tucker (conditions for optimality)

LP

Linear Programming

MBAL

Modified Barrier-Augmented Lagrangian

MCC

Multiple Centrality Corrections

MILP

Mixed Integer Linear Programming

MINLP

Mixed Integer-Nonlinear Programming

MW

Megawatt

NC

Nonlinear Complementarity

NLP

Nonlinear Programming

OPF

Optimal Power Flow

ORPF

Optimal Reactive Power Flow

PC

Predictor-Corrector

PD

Primal-Dual

PDIPM

Primal-Dual Interior Point Method

PDLB

Primal-Dual Logarithmic Barrier

QP

Quadratic Programming

RG

Reduced Gradient

SCED

Security-Constrained Economic Dispatch

SCIPM

Step-Controlled Interior Point Method

SCUC

Security-Constrained Unit Commitment

SDP

Semi-Definite Programming

SLP

Sequential Linear Programming

SQP

Sequential Quadratic Programming

TRIPM

Trust Region Interior Point Method

UPFC

Unified Power Flow Controller

VAR

Volt-Ampere Reactive

References

  1. 1.
    Abadie, J., Carpentier, J.: Generalization of the wolfe reduced gradient method to the case of nonlinear constraints. In: Fletcher, R. (ed.) Optimization, Proceedings of a Symposium Held at University of Keele, 1968, pp. 37–47. Academic Press, London (1969) Google Scholar
  2. 2.
    Acha, E., Fuerte-Esquivel, C., Ambriz-Pérez, H., Angeles-Camacho, C.: FACTS: Modeling and Simulation in Power Networks. Wiley, New York (2004) CrossRefGoogle Scholar
  3. 3.
    Adibi, M., Polyak, R., Griva, I., Mili, L., Ammari, S.: Optimal transformer tap selection using modified barrier-augmented Lagrangian method. IEEE Trans. Power Syst. 18, 251–257 (2003) CrossRefGoogle Scholar
  4. 4.
    Alguacil, N., Conejo, A.: Multiperiod optimal power flow using benders decomposition. IEEE Trans. Power Syst. 15(1), 196–201 (2000) CrossRefGoogle Scholar
  5. 5.
    Almeida, K., Galiana, F.: Critical cases in the optimal power flow. IEEE Trans. Power Syst. 11(3), 1509–1518 (1996) CrossRefGoogle Scholar
  6. 6.
    Alsac, O., Stott, B.: Optimal load flow with steady-state security. IEEE Trans. Power Appar. Syst. PAS-93(3), 745–751 (1974) CrossRefGoogle Scholar
  7. 7.
    Alsac, O., Bright, J., Praise, M., Stott, B.: Further developments in LP-based optimal power flow. IEEE Trans. Power Syst. 5(3), 697–711 (1990) CrossRefGoogle Scholar
  8. 8.
    Avalos, R., Canizares, C., Anjos, M.: A practical voltage-stability-constrained optimal power flow. In: IEEE Power and Energy Society General Meeting—Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–6 (2008) CrossRefGoogle Scholar
  9. 9.
    Azevedo, A., Oliveira, A., Rider, M., Soares, S.: How to efficiently incorporate facts devices in optimal active power flow model. J. Ind. Manag. Optim. 6(2), 315–331 (2010) MATHCrossRefGoogle Scholar
  10. 10.
    Azmy, A.: Optimal power flow to manage voltage profiles in interconnected networks using expert systems. IEEE Trans. Power Syst. 22(4), 1622–1628 (2007) CrossRefGoogle Scholar
  11. 11.
    Bai, X., Wei, H.: Semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints. IET Gener. Transm. Distrib. 3(2), 182–197 (2009) CrossRefGoogle Scholar
  12. 12.
    Bakirtzis, A., Biskas, P.: A decentralized solution to the dc-opf of interconnected power systems. IEEE Trans. Power Syst. 18(3), 1007–1013 (2003) CrossRefGoogle Scholar
  13. 13.
    Bazaraa, M., Sherali, H., Shetty, C.: Nonlinear Programming: Theory and Algorithms. Wiley New York (2006) MATHCrossRefGoogle Scholar
  14. 14.
    Bell, B.: Nonsmooth Optimization by Successive Quadratic Programming. University of Washington (1984) Google Scholar
  15. 15.
    Berizzi, A., Delfanti, M., Marannino, P., Pasquadibisceglie, M., Silvestri, A.: Enhanced security-constrained OPF with FACTS devices. IEEE Trans. Power Syst. 20(3), 1597–1605 (2005) CrossRefGoogle Scholar
  16. 16.
    Biskas, P., Ziogos, N., Tellidou, A., Zoumas, C., Bakirtzis, A., Petridis, V., Tsakoumis, A.: Comparison of two metaheuristics with mathematical programming methods for the solution of OPF. In: Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems (2005) Google Scholar
  17. 17.
    Bollt, S.: Nonlinear Programming by Successive Linear Programming Approximations. Massachusetts Institute of Technology, Dept. of Economics (1964) Google Scholar
  18. 18.
    Burchett, R., Happ, H., Vierath, D., Wirgau, K.: Developments in optimal power flow. IEEE Trans. Power Appar. Syst. PAS-101(2), 406–414 (1982). doi:10.1109/TPAS.1982.317121 CrossRefGoogle Scholar
  19. 19.
    Burchett, R., Happ, H., Wirgau, K.: Large scale optimal power flow. IEEE Trans. Power Appar. Syst. 101(10), 3722–3732 (1982) CrossRefGoogle Scholar
  20. 20.
    Burchett, R., Happ, H., Veirath, D.: Quadratically convergent optimal power flow. IEEE Trans. Power Appar. Syst. 103(11), 3267–3275 (1984) CrossRefGoogle Scholar
  21. 21.
    Capitanescu, F., Wehenkel, L.: Sensitivity-based approaches for handling discrete variables in optimal power flow computations. IEEE Trans. Power Syst. 25(4), 1780–1789 (2010). doi:10.1109/TPWRS.2010.2044426 CrossRefGoogle Scholar
  22. 22.
    Capitanescu, F., Glavic, M., Wehenkel, L.: Experience with the multiple centrality corrections interior-point algorithm for optimal power flow. In: CEE Conference, Coimbra, Portugal (2005) Google Scholar
  23. 23.
    Capitanescu, F., Glavic, M., Ernst, D., Wehenkel, L.: Interior-point based algorithms for the solution of optimal power flow problems. Electr. Power Syst. Res. 77(5–6), 508–517 (2007) CrossRefGoogle Scholar
  24. 24.
    Capitanescu, F., Rosehart, W., Wehenkel, L.: Optimal power flow computations with constraints limiting the number of control actions. In: IEEE Bucharest Power Tech Conference, Bucharest, Romania, pp. 1–8 (2009) CrossRefGoogle Scholar
  25. 25.
    Carpenter, T.J., Lusting, I.J., Mulvey, J.M., Shanno, D.F.: Higher-order predictor-corrector interior point methods with application to quadratic objectives. SIAM J. Optim. 3(4), 696–725 (1993). doi:10.1137/0803036 MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Carpentier: Contribution to the economic dispatch problem. Bull. Soc. Fr. Electr. 8(3), 431–447 (1962) Google Scholar
  27. 27.
    Carpentier, J.: Optimal power flows. Electr. Power Energy Syst. 1(1), 3–15 (1979). doi:10.1016/0142-0615(79)90026-7 CrossRefGoogle Scholar
  28. 28.
    de Carvalho, E., dos Santos, A., Mac, T.: Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem. Appl. Math. Comput. 200, 529–536 (2008) MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Castronuovo, E., Campagnolo, J., Salgado, R.: In: Proceedings of the IEEE/PES T&D 2002 Latin America, São Paulo, Brazil (2002) Google Scholar
  30. 30.
    Chang, S.K., Albuyeh, F., Gilles, M., Marks, G., Kato, K.: Optimal real-time voltage control. IEEE Trans. Power Syst. 5(3), 750–758 (1990) CrossRefGoogle Scholar
  31. 31.
    Chattopadhyay, D., Gan, D.: Market dispatch incorporating stability constraints. Int. J. Electr. Power Energy Syst. 23(6), 459–469 (2001) CrossRefGoogle Scholar
  32. 32.
    Chen, L., Tada, Y., Okamoto, H., Tanabe, R., Ono, A.: Optimal operation solutions of power systems with transient stability constraints. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(3), 327–329 (2001) MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    Chiang, H.D., Wang, B., Jiang, Q.Y.: Applications of TRUST-TECH methodology in optimal power flow of power systems. In: Kallrath, J., Pardalos, P., Rebennack, S., Scheidt, M. (eds.) Optimization in the Energy Industry, Energy Systems, vol. 1, pp. 297–318. Springer, Berlin (2009). Chap. 13 CrossRefGoogle Scholar
  34. 34.
    Chowdhury, E.H., Rahrnan, S.: A review of recent advances in economic dispatch. IEEE Trans. Power Syst. 5(4), 1248–1259 (1990) CrossRefGoogle Scholar
  35. 35.
    Conejo, A., Aguado, J.: Multi-area coordinated decentralized dc optimal power flow. Power Syst. 13(4), 1272–1278 (1998) CrossRefGoogle Scholar
  36. 36.
    Conejo, A.J., Nogales, F.J., Prieto, F.J.: A decomposition procedure based on approximate Newton directions. Math. Program. 93, 495–515 (2002) MathSciNetMATHCrossRefGoogle Scholar
  37. 37.
    Contaxis, G., Delkis, C., Korres, G.: Decoupled optimal load flow using linear or quadratic programming. IEEE Trans. Power Syst. PWRS-I, 1–7 (1986) CrossRefGoogle Scholar
  38. 38.
    da Costa, G.: Optimal reactive dispatch through primal-dual method. IEEE Trans. Power Syst. 12(2), 669–674 (1997). doi:10.1109/59.589644 CrossRefGoogle Scholar
  39. 39.
    da Costa, G., Costa, C., de Souza, A.: Comparative studies of optimization methods for the optimal power flow problem. Electr. Power Syst. Res. 56, 249–254 (2000) CrossRefGoogle Scholar
  40. 40.
    Crisan, D., Mohtadi, M.: Efficient identification of binding inequality constraints in the optimal power flow Newton approach. In: IEE PROCEEDINGS-C, vol. 139, pp. 365–370 (1992) Google Scholar
  41. 41.
    Dai, Y., McCalley, J., Vittal, V.: Simplification, expansion and enhancement of direct interior point algorithm for power system maximum loadability. IEEE Trans. Power Syst. 15(3), 1014–1021 (2000) CrossRefGoogle Scholar
  42. 42.
    Das, J.: Power System Analysis: Short-Circuit Load Flow and Harmonics. CRC Press, Boca Raton (2002) Google Scholar
  43. 43.
    Dent, C., Ochoa, L., Harrison, G., Bialek, J.: Efficient secure AC OPF for network generation capacity assessment. IEEE Trans. Power Syst. 25, 575–583 (2010) CrossRefGoogle Scholar
  44. 44.
    Deuflhard, P.: Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms. Springer, Berlin (2004) MATHGoogle Scholar
  45. 45.
    Dommel, H., Tinney, W.: Optimal power flow solutions. IEEE Trans. Power Appar. Syst. 87(10), 1866–1876 (1968) CrossRefGoogle Scholar
  46. 46.
    El-Hawary, M.: Optimal economic operation of large scale electric power systems: a review. In: Proceedings Joint International Power Conference Athens Power Tech., vol. 1, pp. 206–210 (1993) CrossRefGoogle Scholar
  47. 47.
    Fernandes, R., Happ, H., Wirgau, K.: Optimal reactive power flow for improved system operations. Int. J. Electr. Power Energy Syst. 2(3), 133–139 (1980) CrossRefGoogle Scholar
  48. 48.
    Franch, T., Scheidt, M., Stock, G.: Current and future challenges for production planning systems. In: Kallrath, J., Pardalos, P., Rebennack, S., Scheidt, M. (eds.) Optmization in the Energy Industry, Energy Systems, vol. 1, pp. 5–18. Springer, Berlin (2009). Chap. 1 CrossRefGoogle Scholar
  49. 49.
    Frank, S., Steponavice, I., Rebennack, S.: Optimal power flow: A bibliographic survey, II., Non-deterministic and hybrid methods. Energy Syst. (2012). 10.1007/s12667-012-0057-x Google Scholar
  50. 50.
    Gan, D., Thomas, R., Zimmerman, R.: Stability-constrained optimal power flow. IEEE Trans. Power Syst. 15(2), 535–540 (2000) CrossRefGoogle Scholar
  51. 51.
    Garzillo, A., Innorrta, M., Ricci, M.: The problem of the active and reactive optimum power dispatching solved by utilizing a primal-dual interior point method. Int. J. Electr. Power Energy Syst. 20(6), 427–434 (1998) CrossRefGoogle Scholar
  52. 52.
    Geidl, M., Andersson, G.: Optimal power flow of multiple energy carriers. IEEE Trans. Power Syst. 22(1), 145–155 (2007) CrossRefGoogle Scholar
  53. 53.
    Glavitsch, H., Spoerry, M.: Quadratic loss formula for reactive dispatch. IEEE Trans. Power Appar. Syst. 102(12), 3850–3858 (1983) CrossRefGoogle Scholar
  54. 54.
    Gomez, T., Perez-Arriaga, I., Lumbreras, J., Parra, V.: A security-constrained decomposition approach to optimal reactive power planning. IEEE Trans. Power Syst. 6(3), 1069–1076 (1991) CrossRefGoogle Scholar
  55. 55.
    Gondzio, J.: Multiple centrality corrections in a primal-dual method for linear programming. Comput. Optim. Appl. 6(2), 137–156 (1996) MathSciNetMATHCrossRefGoogle Scholar
  56. 56.
    Granelli, G., Montagna, M.: Security constrained economic dispatch using dual quadratic programming. Electr. Power Syst. Res. 56, 71–80 (2000) CrossRefGoogle Scholar
  57. 57.
    Granville, S.: Optimal reactive dispatch through interior point method. IEEE Trans. Power Syst. 9(1), 136–146 (1994) CrossRefGoogle Scholar
  58. 58.
    Griffith, R., Stewart, R.: A nonlinear programming technique for optimization of continuous processing systems. Manag. Sci. 7, 379–392 (1961) MathSciNetMATHCrossRefGoogle Scholar
  59. 59.
    Grigsby, L.: The Electric Power Engineering Handbook. CRC Press, Boca Raton (2000) CrossRefGoogle Scholar
  60. 60.
    Gross, G., Bompard, E.: Optimal power flow application issues in the pool paradigm. Int. J. Electr. Power Energy Syst. 26(10), 787–796 (2004) Google Scholar
  61. 61.
    Grudinin, N.: Combined Quadratic-Separable programming OPF algorithm for economic dispatch and security control. IEEE Trans. Power Syst. 12(4), 1682–1688 (1997) CrossRefGoogle Scholar
  62. 62.
    Grudinin, N.: Reactive power optimization using successive quadratic programming method. IEEE Trans. Power Syst. 13(4), 1219–1225 (1998) CrossRefGoogle Scholar
  63. 63.
    Happ, H.: Optimal power dispatch—a comprehensive survey. IEEE Trans. Power Appar. Syst. 96(3), 841–854 (1977). doi:10.1109/T-PAS.1977.32397 CrossRefGoogle Scholar
  64. 64.
    Hong, Y.: Enhanced Newton optimal power flow approach: experiences in Taiwan power system. In: IEE Proceedings, vol. 139 (1992) Google Scholar
  65. 65.
    Horst, R., Pardalos, P., Thoai, N.V.: Introduction to Global Optimization, 2nd edn. Springer, Berlin (2000) MATHGoogle Scholar
  66. 66.
    Housos, E., Irisarri, G.: A sparse variable metric optimization method applied to the solution of power system problems. IEEE Trans. Power Appar. Syst. 101(1), 195–202 (1982) CrossRefGoogle Scholar
  67. 67.
    Huneault, M., Galiana, F.: A survey of the optimal power flow literature. IEEE Trans. Power Syst. 6(2), 762–770 (1991) CrossRefGoogle Scholar
  68. 68.
    Iba, K., Suzuki, H., Suzuki, K.I., Suzuki, K.: Practical reactive power allocation/operation planning using successive linear programming. IEEE Trans. Power Appar. Syst. 3(2), 558–566 (1988) CrossRefGoogle Scholar
  69. 69.
    Irisarri, G., Wang, X., Tong, J., Mokhtari, S.: Maximum loadability of power systems using interior point non-linear optimization method. IEEE Trans. Power Syst. 12(1), 162–172 (1997). doi:10.1109/59.574936 CrossRefGoogle Scholar
  70. 70.
    Jabr, R.: Primal-dual interior-point method to solve the optimal power flow dispatching problem. Optim. Eng. 4(4), 309–336 (2003) MathSciNetMATHCrossRefGoogle Scholar
  71. 71.
    Jabr, R.: Optimal power flow using an extended conic quadratic formulation. IEEE Trans. Power Syst. 23(3), 1000–1008 (2008) CrossRefGoogle Scholar
  72. 72.
    Jabr, R.: Recent developments in optimal power flow modeling techniques. In: Rebennack, S., Pardalos, P., Pereira, M., Iliadis, N. (eds.) Handbook of Power Systems, Energy Systems, vol. II, pp. 3–29. Springer, Berlin (2010) CrossRefGoogle Scholar
  73. 73.
    Jabr, R., Coonick, A., Cory, B.: A primal-dual interior point method for optimal power flow dispatching. IEEE Trans. Power Syst. 17(3), 654–662 (2002) CrossRefGoogle Scholar
  74. 74.
    Jamoulle, E., Dupont, G.: A reduced gradient method with variable base using second order information, applied to the constrained- and optimal power flow (2004). www.systemseurope.be/pdf/nap_article-E.pdf. Unpublished, accessed in December 2011
  75. 75.
    Jiang, Q., Han, Z.: Solvability identification and feasibility restoring of divergent optimal power flow problems. Sci. China Ser. E, Technol. Sci. 52(4), 944–954 (2009) MATHCrossRefGoogle Scholar
  76. 76.
    Jiang, Q., Chiang, H., Guo, C., Cao, Y.: Power-current hybrid rectangular formulation for interior-point optimal power flow. IET Gener. Transm. Distrib. 3(8), 748–756 (2009) CrossRefGoogle Scholar
  77. 77.
    Karmarkar, N.: A new polynomial time algorithm for linear programming. Combinatorica 4, 373–395 (1984) MathSciNetMATHCrossRefGoogle Scholar
  78. 78.
    Karoui, K., Platbrood, L., Crisciu, H., Waltz, R.: New large-scale security constrained optimal power flow program using a new interior point algorithm. In: 5th International Conference on European Electricity Market, pp. 1–6 (2008). eEM CrossRefGoogle Scholar
  79. 79.
    Kirschen, D., Meeteren, H.V.: MW/voltage control in a linear programming based optimal power flow. IEEE Trans. Power Syst. 3(2), 481–489 (1988) CrossRefGoogle Scholar
  80. 80.
    Klee, V., Minty, J.G.: How good is the simplex algorithm? Tech. Rep., Washington University (1970) Google Scholar
  81. 81.
    Kundur, P.: Power System Stability and Control. McGraw Hill, New York (1994) Google Scholar
  82. 82.
    Lavaei, J.: Zero duality gap for classical OPF problem convexifies fundamental nonlinear power problems. In: American Control Conference (2011) Google Scholar
  83. 83.
    Lavaei, J., Low, S.H.: Zero duality gap in optimal power flow problem. IEEE Transactions on Power Systems 27(1), 92–107 (2012) CrossRefGoogle Scholar
  84. 84.
    Lehmköster, C.: Security constrained optimal power flow for an economical operation of FACTS-devices in liberalized energy markets. IEEE Trans. Power Deliv. 17(2), 603–608 (2002) CrossRefGoogle Scholar
  85. 85.
    Li, M., Tang, W., Tang, W., Wu, Q., Saunders, J.: Bacterial foraging algorithm with varying population for optimal power flow. In: Applications of Evolutinary Computing. Lectures Notes in Computer Science, pp. 32–41. Springer, Berlin (2007) CrossRefGoogle Scholar
  86. 86.
    Li, X., Li, Y., Zhang, S.: Analysis of probabilistic optimal power flow taking account of the variation of load power. IEEE Trans. Power Syst. 23(3), 992–999 (2008) CrossRefGoogle Scholar
  87. 87.
    Li, Y., McCalley, J.: Risk-based optimal power flow and system operation state. In: IEEE PES General Meeting (2009) Google Scholar
  88. 88.
    Lima, F., Galiana, F., Kockar, I., Munoz, J.: Phase shifter placement in Large-Scale systems via mixed integer linear programming. IEEE Trans. Power Syst. 18(3), 1029–1034 (2003) CrossRefGoogle Scholar
  89. 89.
    Lin, C.H., Lin, S.Y.: Distributed optimal power flow with discrete control variables of large distributed power systems. IEEE Trans. Power Syst. 23(3), 1383–1393 (2008) CrossRefGoogle Scholar
  90. 90.
    Lin, W.M., Huang, C.H., Zhan, T.S.: A hybrid current-power optimal power flow technique. IEEE Trans. Power Syst. 23(1), 177–185 (2008) CrossRefGoogle Scholar
  91. 91.
    Lin, X., David, A., Yu, C.: Reactive power optimization with voltage stability consideration in power market systems. In: IEE Proceedings—Genereration, Transmission and Distribution, vol. 150, pp. 305–310 (2003) Google Scholar
  92. 92.
    Lobato, E., Rouco, L., Navarrete, M., Casanova, R., Lopez, G.: An LP-based optimal power flow for transmission losses and generator reactive margins minimization. In: Proceedings of IEEE Porto Power Tech Conference, Portugal (2001) Google Scholar
  93. 93.
    Lu, N., Unum, M.: Network constrained security control using an interior point algorithm. IEEE Trans. Power Syst. 8(3), 1068–1076 (1993) CrossRefGoogle Scholar
  94. 94.
    Maria, G., Findlay, J.: A Newton optimal power flow program for Ontario hydro EMS. IEEE Trans. Power Syst. 2(3), 576–582 (1987) CrossRefGoogle Scholar
  95. 95.
    Martinez-Crespo, J., Usaola, J., Fernandez, J.: Security-constrained optimal generation scheduling in large-scale power systems. IEEE Trans. Power Syst. 21(1), 321–332 (2006) CrossRefGoogle Scholar
  96. 96.
    Mehrotra, S.: On the implementation of a primal-dual interior-point method. SIAM J. Optim. 2(4), 575–601 (1992) MathSciNetMATHCrossRefGoogle Scholar
  97. 97.
    Min, W., Shengsong, L.: A trust region interior point algorithm for optimal power flow problems. Int. J. Electr. Power Energy Syst. 27(4), 293–300 (2005) CrossRefGoogle Scholar
  98. 98.
    Momoh, J.: A generalized quadratic-based model for optimal power flow. In: Conference Proceedings IEEE International Conference on Systems, Man and Cybernetics, vol. 1, pp. 261–271 (1989) CrossRefGoogle Scholar
  99. 99.
    Momoh, J., Zhu, J.: Improved interior point method for OPF problems. IEEE Trans. Power Syst. 14(3), 1114–1120 (1999) CrossRefGoogle Scholar
  100. 100.
    Momoh, J., Guo, S., Ogbuobiri, E., Adapa, R.: The quadratic interior point method solving power system optimization problems. IEEE Trans. Power Syst. 9(3), 1327–1336 (1994) CrossRefGoogle Scholar
  101. 101.
    Momoh, J., Koessler, R., Bond, M.S., Sun, D., Papalexopoulos, A., Ristanovic, P.: Challenges to optimal power flow. IEEE Trans. Power Syst. 12(1), 444–447 (1997) CrossRefGoogle Scholar
  102. 102.
    Momoh, J.A., El-Hawary, M., Adapa, R.: A review of selected optimal power flow literature to 1993. Part I. Non Linear and quadratic programming approaches. IEEE Trans. Power Syst. 14(1), 105–111 (1999) CrossRefGoogle Scholar
  103. 103.
    Momoh, J.A., El-Hawary, M., Adapa, R.: A review of selected optimal power flow literature to 1993. Part II. Newton, linear programming and interior point methods. IEEE Trans. Power Syst. 14(1), 105–111 (1999) CrossRefGoogle Scholar
  104. 104.
    Monticelli, A., MVFPereira Granville, S.: Security-constrained optimal power flow with post-contingency corrective rescheduling. IEEE Trans. Power Syst. 2(1), 175–180 (1987) CrossRefGoogle Scholar
  105. 105.
    Mota-Palomino, R., Quintana, V.: Sparse reactive power scheduling by a penalty-function-linear programming technique. IEEE Trans. Power Syst. PWRS-I(3), 31–39 (1986) CrossRefGoogle Scholar
  106. 106.
    Moyano, C., Salgado, R.: Adjusted optimal power flow solutions via parameterized formulation. Electr. Power Syst. Res. 80(9), 1018–1023 (2010) CrossRefGoogle Scholar
  107. 107.
    Muchayi, M., El-Hawary, M.: A summary of algorithms in reactive power pricing. Int. J. Electr. Power Energy Syst. 21, 119–124 (1999) CrossRefGoogle Scholar
  108. 108.
    Nocedal, J., Wright, S.: Numerical Optimization, 2nd edn. Springer, Berlin (2006) MATHGoogle Scholar
  109. 109.
    Nogales, F.J., Prieto, F.J., Conejo, A.J.: A decomposition methodology applied to the multi-area optimal power flow problem. Ann. Oper. Res. 120, 99–116 (2003) MathSciNetMATHCrossRefGoogle Scholar
  110. 110.
    Nualhong, D., Chusanapiputt, S., Phomvuttisarn, S., Jantarang, S.: Reactive tabu search for optimal power flow under constrained emission dispatch. In: IEEE Region 10 Conference 2004. TENCON, vol. 3, pp. 327–330 (2004) CrossRefGoogle Scholar
  111. 111.
    de Oliveira, L., Carneiro Jr., S.,de Oliveira, E.J., Pereira, J.L.R., Silva Jr., I.C.,Costa, J.S.: Optimal reconfiguration and capacitor allocation in radial distribution systems for energy losses minimization. Int. J. Electr. Power Energy Syst. 32(8), 840–848 (2010) CrossRefGoogle Scholar
  112. 112.
    Osman, M., Abo-Sinna, M., Mousa, A.: A solution to the optimal power flow using genetic algorithm. Appl. Math. Comput. 155(2), 391–405 (2004) MathSciNetMATHCrossRefGoogle Scholar
  113. 113.
    Pandya, K., Joshi, S.: A survey of optimal power flow methods. J. Theor. Appl. Inf. Technol. 4(5), 450–458 (2008) Google Scholar
  114. 114.
    Papalexopoulos, A., Imparato, C., Wu, F.: Large-scale optimal power flow: effects of initialization, decoupling and discretization. IEEE Trans. Power Syst. 4(2), 748–759 (1989) CrossRefGoogle Scholar
  115. 115.
    Parker, C., Morrison, I., Sutanto, D.: Application of an optimisation method for determining the reactive margin from voltage collapse in reactive power planning. IEEE Trans. Power Syst. 11(3), 1473–1481 (1996) CrossRefGoogle Scholar
  116. 116.
    Patra, S., Goswamib, S.: A non-interior point approach to optimum power flow solution. Electr. Power Syst. Res. 74, 17–26 (2005) CrossRefGoogle Scholar
  117. 117.
    Peschon, J., Bree, D., Hajdu, L.: Optimal power-flow solutions for power system planning. Proc. IEEE 6(1), 64–70 (1972) CrossRefGoogle Scholar
  118. 118.
    Qiu, W., Flueck, A., Tu, F.: A new parallel algorithm for security constrained optimal power flow with a nonlinear interior point method. In: IEEE Power Engineering Society General Meeting, pp. 2422–2428 (2005) CrossRefGoogle Scholar
  119. 119.
    Qiu, Z., Deconinck, G., Belmans, R.: A literature survey of optimal power flow problems in the electricity market context. In: IEEE/PES Power Systems Conference and Exposition. PSCE’09, Seattle, WA, pp. 1–6 (2009) Google Scholar
  120. 120.
    Radziukynas, V., Radziukyniene, I.: Optimization methods application to optimal power flow systems. In: Kallrath, J., Pardalos, P., Rebennack, S., Scheidt, M. (eds.) Optimization in the Energy Industry, Energy Systems, vol. 1, pp. 409–436. Springer, Berlin (2009). Chap. 18 CrossRefGoogle Scholar
  121. 121.
    Ramos, R., Vallejos, J., Barn, B.: Multi-objective reactive power compensation with voltage security. In: Proceedings IEEE/PES Transmission and Distribution Conf. and Expo, Latin America, Brazil, pp. 302–307 (2004) Google Scholar
  122. 122.
    Rashidi, M.A., El-Hawary, M.: Hybrid particle swarm optimization approach for solving the discrete OPF problem considering the valve loading effects. IEEE Trans. Power Syst. 22(4), 2030–2038 (2007) CrossRefGoogle Scholar
  123. 123.
    Rau, N.: Issues in the path toward an RTO and standard markets. IEEE Trans. Power Syst. 18(2), 435–443 (2003) CrossRefGoogle Scholar
  124. 124.
    Rau, N.: Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry. Wiley/IEEE Press, Hoboken (2003) Google Scholar
  125. 125.
    Rider, M., Castro, C., Bedrinana, M., Garcia, A.: Towards a fast and robust interior point method for power system applications. IEE Proc., Gener. Transm. Distrib. 151, 575–581 (2004) CrossRefGoogle Scholar
  126. 126.
    Rider, M., Paucar, V., Garcia, A.: Enhanced higher-order interior-point method to minimise active power losses in electric energy systems. IEE Proc., Gener. Transm. Distrib. 151(4), 517–525 (2004) CrossRefGoogle Scholar
  127. 127.
    Rosehart, W., Canizares, C., Vannelli, A.: Sequential methods in solving economic power flow problems. In: IEEE Canadian Conference on Electrical and Computer Engineering, vol. 1, pp. 281–284 (1997) Google Scholar
  128. 128.
    Rosehart, W., Canizares, C., Quintana, V.: Optimal power flow incorporating voltage collapse constraints. In: Proceedings of the 1999 IEEE/PES Summer Meeting, Edmonton, Alberta, pp. 820–825 (1999) Google Scholar
  129. 129.
    Rosehart, W., Schellenberg, A., Roman, C.: New tools for power system dynamic performance management. In: IEEE Power Engineering Society General Meeting (2006) Google Scholar
  130. 130.
    Sadati, N., Amraee, T., Ranjbar, A.: A global particle Swarm-Based-Simulated annealing optimization technique for under-voltage load shedding problem. Appl. Soft Comput. 9, 652–657 (2009) CrossRefGoogle Scholar
  131. 131.
    Saha, T., Maitra, A.: Optimal power flow using the reduced Newton approach in rectangular coordinates. Int. J. Electr. Power Energy Syst. 20(6), 383–389 (1998) CrossRefGoogle Scholar
  132. 132.
    Salahi, M., Pengy, J., Terlaky, T.: On Mehrotra-type predictor-corrector algorithms. SIAM J. Optim. 18(4), 1377–1397 (2007) MathSciNetMATHCrossRefGoogle Scholar
  133. 133.
    Santos, A., Deckmann, S. Jr., Soares, S.: A dual augmented Lagrangian approach for optimal power flow. IEEE Trans. Power Syst. 3, 1020–1025 (1988) CrossRefGoogle Scholar
  134. 134.
    Sasson, A., Viloria, F., Aboytes, F.: Optimal load flow solution using the Hessian matrix. IEEE Trans. Power Appar. Syst. PAS-92(1), 31–41 (1973). doi:10.1109/TPAS.1973.293590 CrossRefGoogle Scholar
  135. 135.
    Scala, M.L., Trovato, M., Antonelli, C.: On-line dynamic preventive control: an algorithm for transient security constraints. IEEE Trans. Power Syst. 13(2), 601–610 (1998) CrossRefGoogle Scholar
  136. 136.
    Smale, S.: On the average number of steps of the simplex method of linear programming. Math. Program. 27, 241–262 (1983) MathSciNetMATHCrossRefGoogle Scholar
  137. 137.
    Sojoudi, S., Lavaei, J.: Network topologies guaranteeing zero duality gap for optimal power flow problem (2011). Submitted for publication. Available https://www.cds.caltech.edu/~lavaei/TPS_S_L.pdf
  138. 138.
    Sousa, A., Torres, G.: Globally convergent optimal power flow by trust-region interior-point methods. In: Power Tech 2007, Lausanne, Switzerland (2007) Google Scholar
  139. 139.
    Sousa, A., Torres, G., Cañizares, C.: Robust optimal power flow solution using trust region and interior-point methods. IEEE Trans. Power Syst. 26(2), 487–499 (2011). doi:10.1109/TPWRS.2010.2068568 CrossRefGoogle Scholar
  140. 140.
    Stott, B., Hobson, E.: Power system security control calculation using linear programming. Parts I and II. IEEE Trans. Power Appar. Syst. PAS-97, 1713–1731 (1978). doi:10.1109/TPAS.1978.354664 CrossRefGoogle Scholar
  141. 141.
    Stott, B., Marinho, J.: Linear programming for power system network security applications. IEEE Trans. Power Appar. Syst. PAS-98, 837–848 (1979) CrossRefGoogle Scholar
  142. 142.
    Stott, B., Alsac, O., Monticelli, A.: Security analysis and optimization. In: Proceedings of the, IEEE, vol. 75, pp. 1623–1644 (1987) Google Scholar
  143. 143.
    Stott, B., Jardim, J., Alsac, O.: DC power flow revisited. IEEE Trans. Power Syst. 24(3), 1290–1300 (2009). doi:10.1109/TPWRS.2009.2021235 CrossRefGoogle Scholar
  144. 144.
    Subbaraj, P., Rajnarayanan, P.: Optimal reactive power dispatch using self-adaptive real coded genetic algorithm. Electr. Power Syst. Res. 79, 374–381 (2009) CrossRefGoogle Scholar
  145. 145.
    Sun, D., Ashley, B., Brewer, B., Hughes, A., Tinney, W.: Optimal power flow by Newton approach. IEEE Trans. Power Appar. Syst. 103(10), 2864–2880 (1984) CrossRefGoogle Scholar
  146. 146.
    Thomas, W., Dixon, A., Cheng, D., Dunnett, R., Schaff, G., Thorp, J.: Optimal reactive planning with security constraints. In: IEEE Power Industry Computer Application Conference, pp. 79–84 (1995) Google Scholar
  147. 147.
    Thukaram, D., Yesuratnam, G.: Fuzzy—expert approach for voltage-reactive power dispatch. In: IEEE Power India Conference (2006) Google Scholar
  148. 148.
    Tognola, G., Bacher, R.: Unlimited point algorithm for OPF problems. IEEE Trans. Power Syst. 14(3), 1046–1054 (1999) CrossRefGoogle Scholar
  149. 149.
    Tong, X., Zhang, Y., Wu, F.: A decoupled semismooth Newton method for optimal power flow. In: IEEE Power Engineering Society General Meeting (2006) Google Scholar
  150. 150.
    Torres, G., Quintana, V.: An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates. IEEE Trans. Power Syst. 13(4), 1211–1218 (1998) CrossRefGoogle Scholar
  151. 151.
    Torres, G., Quintana, V.: Optimal power flow by a nonlinear complementarity method. IEEE Trans. Power Syst. 15(3), 1028–1033 (2000) CrossRefGoogle Scholar
  152. 152.
    Torres, G., Quintana, V.: On a nonlinear multiple-centrality corrections interior-point method for optimal power flow. IEEE Trans. Power Syst. 16(2), 222–228 (2001) CrossRefGoogle Scholar
  153. 153.
    Torres, G., Quintana, V.: A Jacobian smoothing nonlinear complementarity method for solving optimal power flows. In: PSCC Conference, Sevilla, Spain (2002) Google Scholar
  154. 154.
    Vanderplaats, G.N.: Numerical Optimization Techniques for Engineering Design, 3rd edn. Vanderplaats Research & Development (1999) Google Scholar
  155. 155.
    Vanti, M., Gonzaga, C.: On the Newton interior-point method for nonlinear optimal power flow. In: IEEE Bologna PowerTech Conference, Bologna, Italy (2003) Google Scholar
  156. 156.
    Vargas, L., Quintana, V., Vannelli, A.: A tutorial description of an interior point method and its applications to security-constrained economic dispatch. IEEE Trans. Power Syst. 8(3), 1315–1323 (1993) CrossRefGoogle Scholar
  157. 157.
    Verbič, G., Cañizares, C.: Probabilistic optimal power flow in electricity markets based on a two-point estimate method. IEEE Trans. Power Syst. 21(4), 1883–1893 (2006) CrossRefGoogle Scholar
  158. 158.
    Wallace, S., Fleten, S.E.: Stochastic programming models in energy. In: Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, pp. 637–677. North-Holland, Amsterdam (2003) CrossRefGoogle Scholar
  159. 159.
    Wang, H., Thomas, R.: Towards reliable computation of large-scale market-based optimal power flow. In: Proceedings of the 40th Hawaii International Conference on System Sciences, pp. 1–10 (2007) Google Scholar
  160. 160.
    Wang, H., Murillo-Sanchez, C., Zimmerman, R., Thomas, R.: On computational issues of market-based optimal power flow. IEEE Trans. Power Syst. 22(3), 1185–1193 (2007) CrossRefGoogle Scholar
  161. 161.
    Wang, L., Xiang, N., Wang, S., Huang, M.: Parallel reduced gradient optimal power flow solution. Electr. Power Syst. Res. 17, 229–237 (1989) CrossRefGoogle Scholar
  162. 162.
    Wei, H., Sasaki, H., Yokoyama, R.: An interior point nonlinear programming for optimal power flow problems within a novel data structure. IEEE Trans. Power Syst. 13(3), 870–877 (1998) CrossRefGoogle Scholar
  163. 163.
    Wolf, P.: Methods of nonlinear programming. In: Nonlinear Programming. Wiley, New York (1967) Google Scholar
  164. 164.
    Wood, A., Wollenberg, B.: Power Generation Operation and Control. Wiley, New York (1996) Google Scholar
  165. 165.
    Wright, S.: Primal-dual Interior-point Methods. SIAM, Philadelphia (1997) MATHCrossRefGoogle Scholar
  166. 166.
    Wu, Y.C., Debs, A., Marsten, R.: A direct nonlinear predictor-corrector primaldual interior point algorithm for optimal power flows. IEEE Trans. Power Syst. 9(2), 876–883 (1994) CrossRefGoogle Scholar
  167. 167.
    Xia, X., Elaiw, A.: Optimal dynamic economic dispatch of generation: a review. Electr. Power Syst. Res. 80(8), 975–986 (2010) CrossRefGoogle Scholar
  168. 168.
    Xia, Y., Chan, K.: Dynamic constrained optimal power flow using semi-infinite programming. IEEE Trans. Power Syst. 21(3), 1455–1458 (2006) CrossRefGoogle Scholar
  169. 169.
    Xiao, Y., Song, Y., Liu, C., Sun, Y.: Available transfer capability enhancement using FACTS devices. IEEE Trans. Power Syst. 18(1), 305–312 (2003) CrossRefGoogle Scholar
  170. 170.
    Xie, K., Song, Y.: Optimal spinning reserve allocation with full AC network constraints via a nonlinear interior point method. Electr. Power Compon. Syst. 28(11), 1071–1090 (2000) Google Scholar
  171. 171.
    Yamin, H.Y., Al-Tallaq, K., Shahidehpour, S.M.: New approach for dynamic optimal power flow using Benders decomposition in a deregulated power market. Electr. Power Syst. Res. 65, 101–107 (2003) CrossRefGoogle Scholar
  172. 172.
    Yan, W., Yu, J., Yu, D., Bhattarai, K.: A new optimal reactive power flow model in rectangular form and its solution by predictor corrector primal dual interior point method. IEEE Trans. Power Syst. 21(1), 61–67 (2006) CrossRefGoogle Scholar
  173. 173.
    Yan, X., Quintana, V.: Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances. IEEE Trans. Power Syst. 14(2), 709–717 (1999) CrossRefGoogle Scholar
  174. 174.
    Yehia, M., Ramadan, R., El-Tawail, Z., Tarhini, K.: An integrated technico-economical methodology for solving reactive power compensation problem. IEEE Trans. Power Appar. Syst. 13(1), 54–59 (1998) CrossRefGoogle Scholar
  175. 175.
    Yu, D., Fagan, J., Foote, B., Aly, A.: An optimal load flow study by the generalized reduced gradient approach. Electr. Power Syst. Res. 10, 47–53 (1986). doi:10.1016/0378-7796(86)90048-9 CrossRefGoogle Scholar
  176. 176.
    Yuan, Y.: A review of trust region algorithms for optimization. In: Proceedings of the Fourth International Congress on Industrial and Applied Mathematics, pp. 271–282 (1999) Google Scholar
  177. 177.
    Yuan, Y., Kubokawa, J., Sasaki, H.: A solution of optimal power flow with multicontingency transient stability constraints. IEEE Trans. Power Syst. 18(3), 1094–1102 (2003) CrossRefGoogle Scholar
  178. 178.
    Zehar, K., Sayah, S.: Optimal power flow with environmental constraint using a fast successive linear programming algorithm: application to the Algerian power system. Energy Convers. Manag. 49, 3361–3365 (2008) CrossRefGoogle Scholar
  179. 179.
    Zhang, J.: A successive linear programming method and its convergence on nonlinear problems. Defense Technical Information Center (1983) Google Scholar
  180. 180.
    Zhang, W., Tolbert, L.: Survey of reactive power planning methods. In: IEEE Power Engineering Society General Meeting, vol. 2, pp. 1430–1440 (2005) Google Scholar
  181. 181.
    Zhang, W., Li, F., Tolbert, L.: Review of reactive power planning: objectives, constraints, and algorithms. IEEE Trans. Power Syst. 22(4), 2177–2186 (2007) CrossRefGoogle Scholar
  182. 182.
    Zhang, X., Handschin, E.: Advanced implementation of UPFC in a nonlinear interior-point OPF. IEE Proc., Gener. Transm. Distrib. 148(5), 489–496 (2001) CrossRefGoogle Scholar
  183. 183.
    Zhang, X., Petoussis, S., Godfrey, K.: Nonlinear interior-point optimal power flow method based on a current mismatch formulation. IEE Proc., Gener. Transm. Distrib. 152, 795–805 (2005) CrossRefGoogle Scholar
  184. 184.
    Zhang, X.P.: In: Fundamentals of Electric Power Systems, pp. 1–52. Wiley, New York (2010). doi:10.1002/9780470608555.ch1 Google Scholar
  185. 185.
    Zhang, X.P., Handschin, E., Yao, M.: Modeling of the generalized unified power flow controller (GUPFC) in a nonlinear interior point OPF. IEEE Trans. Power Syst. 16(3), 367–373 (2001) CrossRefGoogle Scholar
  186. 186.
    Zhang, X.P., Rehtanz, C., Pal, B.: Flexible AC Transmission Systems—Modelling and Control. Springer, Berlin (2006) Google Scholar
  187. 187.
    Zhang, X.P., Rehtanz, C., Pal, B.: Power Systems Flexible AC Transmission Systems: Modelling and Control. Springer, Berlin (2006) Google Scholar
  188. 188.
    Zhang, Y., Ren, Z.: Optimal reactive power dispatch considering costs of adjusting the control devices. IEEE Trans. Power Syst. 20(3), 1349–1356 (2005) MathSciNetCrossRefGoogle Scholar
  189. 189.
    Zhu, J.: Optimization of Power System Operation. Wiley, New York (2009) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Stephen Frank
    • 1
  • Ingrida Steponavice
    • 2
  • Steffen Rebennack
    • 3
  1. 1.Department of Electrical Engineering and Computer ScienceColorado School of MinesGoldenUSA
  2. 2.Department of Mathematical Information TechnologyUniversity of JyvaskylaAgoraFinland
  3. 3.Division of Economics and BusinessColorado School of MinesGoldenUSA

Personalised recommendations